I understand that the redness of the moon during the total lunar eclipse last night/this morning (April 14-15 2014) is a reflection of the red light caused in earth's atmosphere due to Rayleigh scattering (basically, a reflection of all the sunsets and sunrises happening around the earth). Because of this, it seems to me that the moon will appear red during every total lunar eclipse that happens. Is this the case, or are there some lunar eclipses where the moon does not turn red? If it is the case that all total lunar eclipses produce a red moon, why was the media so hyped up about last night's eclipse producing a red moon? Was it especially red?
No, not all total lunar eclipses will turn the Moon deep red. Most of them do, but not all.
If you were standing on the Moon during the eclipse, you'd see the Earth passing in front of, and obscuring, the Sun. But the Earth will never become fully dark, even when the Sun is fully covered. A bright ring will always surround the Earth. Why?
That ring is sunlight refracted by the atmosphere. It's there because the Earth has an atmosphere. You could say it's all the sunrises and sunsets of the Earth, all seen at once. It's this light that continues to illumine the Moon during the eclipse.
But why is the Moon red, instead of some other color? This is because the blue end of the spectrum is scattered more easily in all directions (same mechanism that explains why the sky is blue on Earth), whereas the red part of the spectrum is scattered less easily and moves on a straighter path along the refraction lines. The bright ring around the Earth, as seen from the Moon, is probably red, because most of the blue in it has been scattered away.
Now, if the Earth's atmosphere is full of dust particles from huge volcanic eruptions, the bright ring is a lot weaker. That makes the Moon during the eclipse a much darker shade of red. Sometimes the Moon is a very dark, dull grey during the eclipse, no red hue at all - so dark in fact that it's hard to see in the sky while the eclipse is full. This has happened some decades ago after the Pinatubo eruption.
A measure of the brightness and color of a lunar eclipse is the Danjon scale. Eclipses are rated between 0 (almost invisible, black or very dark grey) and 4 (bright orange with bluish rim).
My estimate is that the last eclipse was a 3.
I can't find a list of recent eclipses rated on a Danjon scale, but here's a list of 20th century eclipses, with a measure of the magnitude of the umbra.
As you can see, the magnitude varies quite a bit.
Bottom line: each eclipse is a bit different. A majority would have some kind of orange, copper or red tint. A minority are too dark to see any color. Unusual colors (outside of the red-yellow interval) are very rarely possible. Brightness and hue varies from one instance to another, since it depends on Earth's atmosphere, which is a system that changes greatly over time.
The redness of the moon is due to Earth's atmosphere refraction of Sun rays and pollution - dust particles etc. The intensity of the colouring will depend on the path the moon takes through the Earth's corona. If it goes right through the middle then we will see a darker moon, while if it travels close to the edges then the influence of refraction and pollution will be greater and thus a redder moon.
Pretty most all lunar eclipses will turn the moon red like that. The amount of redness does vary, and sometimes so little light gets to the sun it is almost completely dark. However the redness is so typical of a lunar eclipse that NASA describes it as a "characteristic orange-red color". That link has a neat table with a categorization of the colour ranges.
Probably what triggered the media's "do a story on that!" bells was lots of chatter they noticed online, mostly from the loony fringe making more of it than it deserves.
The reason for the extra attention was probably because this lunar eclipse (I can't bring myself to write 'blood moon' ick I've done it) is coincident with the Jewish Passover - not a surprising event, as Passover is always when the moon is full after the spring equinox. It happens that the Passover that was celebrated the evening before the day Jesus was executed was followed by a lunar eclipse, and the Bible makes mention of 'the moon being turned to blood.' Simple and straightforward, but then some people start going off on their own weird supposes and imagining that Jesus' second coming will occur on another lunar eclipse, as if a lunar eclipse after the spring equinox was the only time it is possible for him to visit. So you get lots of internet chatter, the media notices what is trending on twitter and does a half-baked story.
Lunar eclipse will occur in other months too, but without this association, people don't seem to care as much.